TY - JOUR
T1 - Linear Restriction Estimates for Schrödinger Equation on Metric Cones
AU - Zhang, Junyong
N1 - Publisher Copyright:
© 2015, Taylor & Francis Group, LLC.
PY - 2015/6/3
Y1 - 2015/6/3
N2 - In this paper, we study some modified linear restriction estimates of the dynamics generated by Schrödinger operator on metric cone M, where the metric cone M is of the form M = (0, ∞)r × Σ, with the cross section Σ being a compact (n − 1)-dimensional Riemannian manifold (Σ, h) and the equipped metric being g = dr2 + r2h. Assuming the initial data possesses additional regularity in angular variable θ ∈ Σ, we show some linear restriction estimates for the solutions. In terms of their applications, we obtain global-in-time Strichartz estimates for radial initial data and show small initial data scattering theory for the mass-critical nonlinear Schrödinger equation on two-dimensional metric cones.
AB - In this paper, we study some modified linear restriction estimates of the dynamics generated by Schrödinger operator on metric cone M, where the metric cone M is of the form M = (0, ∞)r × Σ, with the cross section Σ being a compact (n − 1)-dimensional Riemannian manifold (Σ, h) and the equipped metric being g = dr2 + r2h. Assuming the initial data possesses additional regularity in angular variable θ ∈ Σ, we show some linear restriction estimates for the solutions. In terms of their applications, we obtain global-in-time Strichartz estimates for radial initial data and show small initial data scattering theory for the mass-critical nonlinear Schrödinger equation on two-dimensional metric cones.
KW - Linear restriction estimate
KW - Metric cone
KW - Strichartz estimate
UR - http://www.scopus.com/inward/record.url?scp=84937202396&partnerID=8YFLogxK
U2 - 10.1080/03605302.2014.1003388
DO - 10.1080/03605302.2014.1003388
M3 - Article
AN - SCOPUS:84937202396
SN - 0360-5302
VL - 40
SP - 995
EP - 1028
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 6
ER -